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Why x-t correlation may be important for HBT

Why x-t correlation may be important for HBT Origin of a large&positive x-t correlation: partonic? resonance decays? hadronic rescatterings? Can a (hydro-type) negative x-t correlation survive decays/rescatterings in a transport model? Rout/Rside:

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Why x-t correlation may be important for HBT

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  1. Why x-t correlation may be important for HBT Origin of a large&positive x-t correlation: partonic? resonance decays? hadronic rescatterings? Can a (hydro-type) negative x-t correlation survive decays/rescatterings in a transport model? Rout/Rside: from Gaussian fit vs from emission function Strong and positive x-t correlation and its effect on Rout/Rside Zi-Wei Lin The Ohio State University

  2. HBT Radii fromEmission function S(x,p)or correlation function C(q) . 2 Pratt,PRL84 2) Often use 4-parameter fit for C(q) w/o Coulomb effects: 1) Curvature at q=0: Dx,y=<x*y>-<x><y> If source is Gaussian in space-time, then: Pratt,PRL84 Wiedemann,PRC57 Rsource,ij=Rfit,ij

  3. Study HBT with a transport model Advantage: freezeout in transport is natural as the mean free path grows too big compared with system size How to relate to hydro calculations (Cooper-Frye formula at a sharp hypersurface is usually imposed)

  4. Structure of AMPT model with String Melting HIJING energy in strings and minijet partons A+A Fragment excited strings into partons ZPC (Zhang's Parton Cascade) Till Parton freezeout Coalescence into hadrons ART (A Relativistic Transport model for hadrons) Decay all resonances; Final particle spectra

  5. From Gaussian fits to 3-d correlation function C(q) Au+Au at 130AGeV (b=0 fm) ZWL,Ko&Pal,PRL89

  6. Why x-t correlation may be important? x-t correlation duration-time Spatial-size Magnitude and sign of x-t correlation are important for Rout, Rout/Rside, & extraction of duration-time

  7. Correlations in pion emission source: out-side out-t ZWL,Ko&Pal,PRL89 <Xout (t)> x-t correlation Duration time Spatial-size Source Values: (17fm)**2 = 185 -2*168 + 431 Positive and large, tends to reduce Rout Note:includes  decays

  8. K emission source (excludes  decays): out-side out-t ZWL&Ko,JPG29 <Xout (t)> K source Values: (3.4fm)**2 = 35 -2*22 + 20 also positive and large for K

  9. Turn off  decays to study HBT radii from the emission function • Test hydro-like negative x-t correlation upon hadron formation in AMPT

  10. Pions at freezeout mostly partons ~volume emission ~surface emission y x xside xout <xout> >0 parton transverse flow

  11. x-t correlation for pions Au+Au at 200AGeV (b=0 fm)

  12. Already present for quarks x-t correlation for pions Au+Au at 200AGeV (b=0 fm)

  13. Effect of decays on source radii Hadronic decays produce mt-dependence in Rout & Rside

  14. Rout/Rside from emission function

  15. Can an initial negative x-t correlation survive later? Test negative x-t correlation from hydro models at RHIC energies

  16. Initial hadrons: large initial Rout/Rside ratio (source)

  17. Final hadrons: large final Rout/Rside ratio (source) Negative x-t term becomes positive after hadronic scatterings

  18. Radii are different from source or from Gaussian fit to C(Q) Hardtke&Voloshin, PRC61

  19. AMPT: Au+Au at 200AGeV at b=0 fm, 3mb from source from C(Q) fit Rout/Rside=1 big decrease for fitted Rout, Rout/Rside

  20. With an initial negative x-t correlation at hadron formation from source from C(Q) fit Rout/Rside=1 huge decrease for fitted Rout & Rout/Rside Rout/Rside >>1 ~=1

  21. HBT summary • Strong and positive xout-t correlation term • tends to reduce Rout and Rout/Rside. • already present at parton freezeout/hadron formation • An initial negative x-t correlation can lead to large Rout/Rside (when evaluated from emission function) • Rout/Rside:>1 from emission function ~=1 from Gaussian fits to C(Q). • Even with an large initial negative x-t (with Rout/Rside >>1 from the emission function) • Further investigation is needed to find the reason.

  22. v2(pt) for AuAu at 130A GeV: eta (-0.3, 0.3), minimum bias (b=0-13 fm in AMPT) ZWL&Ko,PRC65

  23. 1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:

  24. - correlation function (w/o Coulomb effects): data corrected for Coulomb effects

  25. Fitted radius parameters vs parton cross sections

  26. Ratio from source >1 > ratio from fit (~=1)

  27. 10 mb results Kaon: source radii~fitted radii MT-scaling for fitted R? ZWL&Ko,JPG29

  28. Zi-Wei Lin The Ohio State University Summary: We study two-pion interferometry at RHIC energies using a multi-phase transport (AMPT) transport model. Strong and positive x-t correlation at kinetic freezeout is present already at the end of the partonic stage, and it remains after hadronic decays and after hadronic interactions. This positive x-t term tends to reduce Rout/Rside when they are evaluated from the space-time widths of the emission source. Moreover, when they are evaluated from Gaussian fits to the 3-d correlation function C(Q), values of Rout/Rside are found to decrease in general and become consistent with one.

  29. x-y distributions at freezeout

  30. Xout-Xside distributions at freezeout

  31. Can an initial negative x-t correlation survive later? Negative x-t term expected at RHIC energies from Cooper-Frye used in hydro models Toy model: hadron formation at surface rt*rt+t*t=(10fm)^2

  32. Negative x-t term becomes positive after hadronic scatterings

  33. With an initial negative x-t correlation at: rt*rt+t*t=(10fm)^2 from source from C(q) fit

  34. With an initial negative x-t correlation but at a larger surface: rt*rt+t*t=(20fm)^2

  35. due to larger initial surface of hadron formation: rt*rt+t*t=(20fm)^2

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